Both the user manuals will give an appropriate minimum distance. Most often, the distance specced in the range's manual will be a standardized distance reflective of using a basic hood you can pick up at an Lowe's or HD that mounts to the underside of a short set of cabinets above the range (usually ~48"). In your case, it sounds like you are going with a pro style hood, so you will need to go with what is specced in the hood manual (usually ~30-36").

Here's a a good thread on this subject concerning 2 other brands of pro range/cooktop & hood (KA & GE Monogram)...

Determining the proper height for your vent hood can be simple as long as you know the height of your ceiling. Let say for example that your ceilings are 9ft high, thatÃ¯Â¿Â½s 108 inches. You would then take the total 108 inches and deduct 36 inches for the height of your range leaving you 72 inches. Then you will need to determine how high you would like your range hood off of your cooktop. Modern-AireÃ¯Â¿Â½s minimum hanging height is 30' above the cooking surface with a maximum installed height of 36' above the cooking surface. Modern-Aire recommends hanging your vent hood 32 - 34 inches above the cooking surface for optimal performance, so letÃ¯Â¿Â½s just say that you have decided to hang it 33 inches above the cooking surface. You have 72 inches remaining, so deduct the 33 inches for the distance between your cooking surface and the bottom of your range hood and you now have a total hood height of 39 inches.